Fluid Instabilities: Viscous Fingering and Stability Analysis

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Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.

Explores nonlinear dynamics, bifurcations, stability, weakly nonlinear systems, saturation, Hopf bifurcation, and global stability analysis.

Explores fluid instability through linearized equations and dispersion relation, analyzing stability based on wavenumber and frequency.

Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.

Covers the concept of fold bifurcation in dynamical systems, focusing on the saddle-mode behavior.

Explores flip and Andronov-Hopf bifurcations, showing how systems change equilibrium points and stability.

Explores transcritical bifurcations and the dynamics near critical points.

Covers the topic of bifurcations in dynamical system theory, focusing on the pitchfork bifurcation.

Explores Rayleigh-Taylor instability, perturbation linearization, boundary conditions, normal mode expansion, and Laplace equation solution.

Explores fluid instabilities, focusing on Rayleigh-Benard analysis and key concepts like buoyancy and temperature gradients.